Tony Hall will be a huge loss to the Royal Opera House, an organisation that, since his appointment 2001, he has effectively turned around. It is hard to imagine, from the purview of 2012, just what a damaged place it was that Hall inherited. At the end of the 1990s, the House was riven with disasters: a succession of artistic directors was crushed by the pressure, a whole board resigned, there were appalling funding problems, and the place was perceived as elitist and out of touch. Now it seems to purr along like a luxury motorcar. The best that can be said for Hall's regime is that the Royal Opera House – despite recurring questions about its role as the most subsidised of all the English arts organisations – now hits the headlines for the brilliance of its ballet and opera rather than for teetering on the brink of collapse.

Genial and soft-spoken, his voice hinting at his Birkenhead upbringing, Hall, 61, is an unflappable figure: thoughtful, polite, clear-headed reassuring. His temperament has stood him in good stead in an environment of big egos and will no doubt do so at the BBC.

From day one, Hall's interests have lain in opening up the Royal Opera House, shaking the stain of elitism. It hasn't always worked: the place is still castigated for high ticket prices and it's hard to ignore the atmosphere of wealth and privilege that lingers in the Floral Hall in the intervals of those heady evenings of dance or opera. But that's only half the story: under his leadership it has made huge efforts to reduce ticket prices at the lower end (they start at £4). There have been huge strides in opening up performances for schools and families, and extremely successful community and outreach initiatives. The companies have worked in ways unimaginable in a stuffier past: the Royal Ballet has danced at the O2, for example. The scheme closest to his heart is in Thurrock, in Kent – the site of the Royal Opera's Production Park, and the locale of deep community engagement. He has spearheaded the Opera House's forays into the digital and film worlds, with cinema broadcasts and education work promoted on iTunesU. The one that got away was his vision of a Royal Opera House in Manchester, which he believed would help the ROH fulfill its destiny as a truly national organisation: the financial collapse put paid to that.

In recent years his interests have taken him increasingly outside the Royal Opera House's four walls. He was appointed chair of the Cultural Olympiad and brought a faltering initiative back on track. He produced a government report on dance in secondary school, quietly but effectively championing the cause of the arts in mainstream British education.

The BBC, it goes without saying, is vastly larger, more complex and more exposed organisation than the Royal Opera House. As troubles go, the BBC is surely in more disarray than was even the Opera House a decade ago. But, as a former BBC head of news, Hall more than knows the ropes. For the Royal Opera House, his departure is bad news: but he will leave an organisation more or less as healthy as it could be. The one comfort will be that under his leadership, the BBC is unlikely to neglect its responsibilities towards music and the arts: when all else is said, Hall is a man who is nutty about opera and ballet.